Crosstalk (or inter-channel interference) is a major source of channel impairment for Multiple Input Multiple Output (MIMO) wired communication systems, such as Digital Subscriber Line (DSL) communication systems.
As the demand for higher data rates increases, DSL systems are evolving toward higher frequency bands, wherein crosstalk between neighboring transmission lines (that is to say transmission lines that are in close vicinity over part or whole of their length, such as twisted copper pairs in a cable binder) is more pronounced (the higher frequency, the more coupling).
Different strategies have been developed to mitigate crosstalk and to maximize effective throughput, reach and line stability. These techniques are gradually evolving from static or dynamic spectral management, techniques to multi-user signal coordination (or vectoring).
One technique for reducing inter-channel interference is joint signal preceding: the transmit data symbols are jointly passed through a precoder before being transmitted over the respective communication channels. The precoder is such that the concatenation of the precoder and the communication channels results in little or no inter-channel interference at the receivers.
A further technique for reducing inter-channel interference is joint signal post-processing: the received data symbols are jointly passed through a postcoder before being detected. The postcoder is such that the concatenation of the communication channels and the postcoder results in little or no inter-channel interference at the receivers.
The choice of the vectoring group, that is to say the set of communication lines, the signals of which are jointly processed, is rather critical for achieving good crosstalk mitigation performances. Within a vectoring group, each communication line is considered as a disturber line inducing crosstalk into the other communication lines of the group, and the same communication line is considered as a victim line receiving crosstalk from the other communication lines of the group. Crosstalk from lines that do not belong to the vectoring group is treated as alien noise and is not canceled.
Ideally, the vectoring group should match the whole set of communication lines that physically and noticeably interact with each other. Yet, local loop unbundling (imposed by national regulation policies) and/or limited vectoring capabilities may prevent such an exhaustive approach, in which case the vectoring group would include a sub-set only of all the physically interacting lines, thereby yielding limited vectoring gains.
Signal vectoring is typically performed within an access node, wherein all the data symbols concurrently transmitted over, or received from, all the communication lines of the vectoring group are available. For instance, signal vectoring is advantageously performed within a Digital Subscriber Line Access Multiplexer (DSLAM) deployed at a Central Office (CO) or as a fiber-fed remote unit closer to subscriber premises (street cabinet, pole cabinet, building cabinet, etc). Signal precoding is particularly appropriate for downstream communication (toward customer premises), while signal post-processing is particularly appropriate for upstream communication (from customer premises).
Linear signal precoding and post-processing are advantageously implemented by means of matrix products.
For instance, a linear precoder performs a matrix-product of a vector of transmit frequency samples with a precoding matrix, the precoding matrix being such that the overall channel matrix is diagonalized, meaning the off-diagonal coefficients of the overall channel, and thus the inter-channel interference, mostly reduce to zero. Practically, and as a first order approximation, the precoder superimposes anti-phase crosstalk pre-compensation signals over the victim line along with the direct signal that destructively interfere at the receiver with the actual crosstalk signals from the respective disturber lines.
Similarly, a linear postcoder performs a matrix-product of a vector of received frequency samples with a crosstalk cancellation matrix, the crosstalk cancellation matrix being such that the overall channel matrix is diagonalized too.
It is of utmost importance thus to get an accurate estimate of the actual crosstalk channels in order to appropriately initialize or update the coefficients of the preceding matrix or of the crosstalk cancellation matrix. In the recommendation entitled “Self-FEXT Cancellation (Vectoring) For Use with VDSL2 Transceivers”, ref, G.993.5, and adopted by the International Telecommunication Union (ITU) on April 2010, the transceivers are configured to send downstream and upstream pilot sequences over the so-called SYNC symbols, which occur periodically after every 256 DATA symbols.
On a given victim line, error samples, which comprise both the real and imaginary part of the slicer error (or receive error vector) as measured for a specific SYNC symbol on a per tone or group-of-tones basis, are reported to a vectoring controller for further crosstalk estimation. The error samples are correlated with a given pilot sequence transmitted over a given disturber line in order to obtain the crosstalk coefficient from that disturber line. To reject the crosstalk contribution from the other disturber lines, the pilot sequences are made orthogonal to each other, for instance by using Walsh-Haclamard sequences comprising ‘+1’ and ‘−1’ anti-phase symbols. The crosstalk estimates are used for initializing or updating the coefficients of the precoding matrix or of the crosstalk cancellation matrix.
Once new coefficients are in force in the precoder or postcoder, the residual crosstalk continue to be tracked, being on account of a crosstalk channel variation, a residual error in the crosstalk estimates, or an approximation in the determination of the precoder or postcoder coefficients. This is typically achieved by means of iterative update methods that gradually converge towards the optimal precoder or postcoder coefficients.
In the idealized linear model, orthogonal pilot sequences as per G.993.5 recommendation are very effective and always produce accurate and unbiased estimates of the crosstalk channels (initialization) or of the residual crosstalk channels (tracking). Yet, due to non-linear effects, the crosstalk estimates can have an undesired offset (or bias) that drives the precoder or postcoder coefficients away from their optimal values.
In high crosstalk environments for instance, the sum of the crosstalk vectors from all the pilot symbols transmitted over all the disturber lines can be such that the received frequency sample goes beyond the decision boundary of the demodulator. If so, the error vector is reported against the wrong constellation point, yielding an offset in the estimate of the nominal or residual crosstalk channel.
In G.993.5 recommendation, the transmit vector is estimated by the receiver. The set of vectors that can be used as pilots is restricted to two states: a normal state (+1) and an inverted state (−1), which is equivalent to Binary Phase Shift Keying (BPSK) modulation. The receiver determines the expected transmit vector by determining in which half-plane the receive vector is, and by selecting the corresponding constellation point as the most probable transmit vector (minimum distance criteria). This operation is referred to as demapping. Alternatively, Quadrature Phase Shift Keying (QPSK or 4-QAM) constellation grid can be used for pilot, detection (although only 2 constellation points out the possible 4 are effectively used), in which case demapping is based on determining the most probable quadrant.
In the event of demapping errors, that is to say when the receiver selects a constellation point different from the transmit, constellation point, the reported slicer error has a completely wrong value. This leads to major inaccuracies in the calculation of the crosstalk coefficients, and thus of the precoder and postcoder coefficients, as the vectoring controller is unaware of the fact that a demapping error has occurred within the receiver.
A possible known solution for dealing with demapping errors would be to use multiple demapping decisions across multiple tones. Given that all probe tones in a particular SYNC symbol are all modulated with the same particular bit from of a given pilot sequence, one can use multiple tones to do a joint estimation. This technique is more robust than the straightforward per-tone decision, but in very low Signal to Noise Ratio (SNR) environments, the receiver could still make a wrong decision. If Frequency Dependent Pilot Sequence (FDPS) is used, the technique can still be applied, using the fact that the pilot values repeat periodically after a given number of tones.
Yet, experiments in the field indicate that at least some receiver models keep on using per-tone decision, with either a BP5K or 4-QAM demodulation grid, thereby increasing the likelihood of demapping errors.
Another example of non-linear effects is signal clipping. Still in high crosstalk environments, the sum of the crosstalk vectors from all the pilot, symbols transmitted over all the disturber lines can be such that the receive frequency sample goes beyond the maximum value supported by the digital processing logic. The error samples would then carry a wrong bounded value that would severely affect and bias the crosstalk estimation process.
Another example of non-linear effects is quantization at various points in the signal path. Quantization makes that these signals can only use certain values. This leads to an offset in the estimate of the residual crosstalk channel.
Using long-term periodic pilots may thus cause biases to build up and may lead to performance degradation over time and instability.